The paper addresses the problem of solving overdetermined systems of linear equations by means of methods of robust estimations, which eliminate the effect of outliers on the estimation results. The process of estimating a vector of parameters was accomplished by means of circular in structure neural networks. Formulating the problem in the aspect of a method for estimating parameters requires formulating an energy function (objective function) whose form was modified by means of a determined weighting function. In the final part of the paper the effectiveness of the methods described was evaluated in terms of controlling and diagnosing a geodetic observation system. The article is merely an introduction to a broadly understood problem of geodetic uses of robust estimators.

An increased use of global navigation techniques for positioning, and in particular for height determination, led to a growing need for precise models of height reference surface, i.e. geoid or quasigeoid. Geoid or quasigeoid heights at a cm accuracy level, provided on growing number ofGPS/levelling sites, can not only be used for quality control of gravimetric geoid but they also can be integrated with gravity data for geoid/quasigeoid modelling. Such a model is of particular use for surveying practice. A method of quasigeoid modelling based on GPS/levelling data with support of geopotential model and gravity data was developed. The components of height anomaly are modelled with the deterministic part that consists of height anomaly based on EGM96 geopotential model and Molodensky's integral, as well as the polynomial representing trend, and from the stochastic part represented by the isotropic covariance function. Model parameters, i.e. polynomial coefficients and covariance function parameters are determined in a single process of robust estimation, resistant to the outlying measurements. The method was verified using almost a thousand height anomalies from the sites of the EUREF-POL, POLREF, EUVN'97 and WSSG (Military Satellite Geodetic Network) networks in Poland as well as geopotential model refined with gravity data in l' x l' grid. The estimated average mean square error of quasigeoid height is at the level of O.Ol m. The outlying measurements were efficiently detected.

A microgrid is an appropriate concept for urban areas with high penetration of renewable power generation, which improves the reliability and efficiency of the distribution network at the consumer premises to meet various loads such as domestic, industrial, and agricultural types. Microgrids comprising inverter-based and synchronous generator-based distribution generators can lead to the instability of the system during the islanded mode of operation. This paper presents a study on designing stable microgrids to facilitate higher penetration of solar power generation into a distribution network. Ageneralized small signal model is derived for a microgrid with static loads, dynamic loads, energy storages, solar photovoltaic (PV) systems, and diesel generators, incorporating the features of dynamic systems. The model is validated by comparing the transient curves given by the model and a transient simulator subjected to step changes. The result shows that full dynamic models of complex systems of microgrids can be built accurately, and the proposed microgrid is stable for all the considered loading situations and solar PV penetration levels according to the small signal stability analysis.

As a result of the development of modern vehicles, even higher accuracy standards are demanded. As known, Inertial Navigation Systems have an intrinsic increasing error which is the main reason of using integrating navigation systems, where some other sources of measurements are utilized, such as barometric altimeter due to its high accuracy in short times of interval. Using a Robust Kalman Filter (RKF), error measurements are absorbed when a Fault Tolerant Altimeter is implemented. During simulations, in order to test the Nonlinear RKF algorithm, two kind of measurement malfunction scenarios have been taken into consideration; continuous bias and measurement noise increment. Under the light of the results, some recommendations are proposed when integrated altimeters are used.

In the paper we present robust estimation methods based on bounded innovation propagation filters and quantile regression, applied to measure Value at Risk. To illustrate advantage connected with the robust methods, we compare VaR forecasts of several group of instruments in the period of high uncertainty on the financial markets with the ones modelled using traditional quasi-likelihood estimation. For comparative purpose we use three groups of tests i.e. based on Bernoulli trial models, on decision making aspect, and on the expected shortfall.

The work presents the results of studies on dependence of effectiveness of chosen robust estimation methods from the internal reliability level of a geodetic network. The studies use computer-simulated observation systems, so it was possible to analyse many variants differing from each other in a planned way. Four methods of robust estimation have been chosen for the studies, differing substantially in the approach to weight modifications. For comparative reasons, the effectiveness studies have also been conducted for the very popular method in surveying practice, of gross error detection basing on LS estimation results, the so called iterative data snooping. The studies show that there is a relation between the level of network internal reliability and the effectiveness of robust estimation methods. In most cases, in which the observation contaminated by a gross error was characterized by a low index of internal reliability, the robust estimation led to results being essentially far from expectations.

The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011–2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-M split estimation, which allows to estimate a vector of parameter differences and the Shift- M split (+) that is a generalisation of Shift- M split estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2 nd , 3 rd and 4 th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.

Generally, gross errors exist in observations, and they affect the accuracy of results. We review methods to detect the gross errors by Robust estimation method based on L1-estimation theory and their validity in adjustment of geodetic networks with different condition. In order to detect the gross errors, we transform the weight of accidental model into equivalent one using not standardized residual but residual of observation, and apply this method to adjustment computation of triangulation network, traverse network, satellite geodetic network and so on. In triangulation network, we use a method of transforming into equivalent weight by residual and detect gross error in parameter adjustment without and with condition. The result from proposed method is compared with the one from using standardized residual as equivalent weight. In traverse network, we decide the weight by Helmert variance component estimation, and then detect gross errors and compare by the same way with triangulation network In satellite geodetic network in which observations are correlated, we detect gross errors transforming into equivalent correlation matrix by residual and variance inflation factor and the result is also compared with the result from using standardized residual. The results of detection are shown that it is more convenient and effective to detect gross errors by residual in geodetic network adjustment of various forms than detection by standardized residual.

The summary of research activities concerning general theory and methodology performed in Poland in the period of 2015–2018 is presented as a national report for the 27th IUGG (International Union of Geodesy and Geophysics) General Assembly. It contains the results of research on new or improved methods and variants of robust parameter estimation and their application, especially to control network analysis. Reliability analysis of the observation system and an integrated adjustment approach are also given. The identifiability (ID) index as a new measure for minimal detectable bias (MDB) in the observation system of a network, has been introduced. A new method of covariance function parameter estimation in the least squares collocation has been developed. The robustified version of the Shift-Msplit estimation, termed as Shift-M*split estimation, which enables estimation of parameter differences (robustly), without the need of prior estimation of the parameters, has been introduced. Results on the analysis of geodetic time series, particularly Earth orientation parameter time series, geocenter time series, permanent station coordinates and sea level variation time series are also provided in this review paper. The entire bibliography of related works is provided in the references.

In the paper issues related to the design of a robust adaptive fuzzy estimator for a drive system with a flexible joint is presented. The proposed estimator ensures variable Kalman gain (based on the Mahalanobis distance) as well as the estimation of the system parameters (based on the fuzzy system). The obtained value of the time constant of the load machine is used to change the values in the system state matrix and to retune the parameters of the state controller. The proposed control structure (fuzzy Kalman filter and adaptive state controller) is investigated in simulation and experimental tests.

The paper presents results of studies on linear synchronous motors controlled in CNC feed axes through an intelligent digital servodrive. The research includes a conceptual design of an open servodrive control system and identification of dynamic models of a test stand with an open CNC system. Advantages of robust control over the classic one are discussed. A hybrid predictive approach to robust control of milling machine X-Y table velocity is proposed and results of simulation tests are presented. Was prepared during the work for the Ministry of Science and Higher Education grant number N N502 336936, (acronym for this project is M.A.R.I.N.E. multivariable hybryd ModulAR motIon coNtrollEr), while its main purpose is the development of new rob ust position/velocity model-based control system, as well as to introduce the measurement of the actual state into the switching algorithm between the locally synthesized controllers. Such switching increases the overall robustness of the machine tool feed-drive module. The paper is the extended version of material proposed in [10].

The paper discusses some of the recent advances in kriging based worst-case design optimisation and proposes a new two-stage approach to solve practical problems. The efficiency of the infill points allocation is improved significantly by adding an extra layer of optimisation enhanced by a validation process.

The accuracy and reliability of Kalman filter are easily affected by the gross errors in observations. Although robust Kalman filter based on equivalent weight function models can reduce the impact of gross errors on filtering results, the conventional equivalent weight function models are more suitable for the observations with the same noise level. For Precise Point Positioning (PPP) with multiple types of observations that have different measuring accuracy and noise levels, the filtering results obtained with conventional robust equivalent weight function models are not the best ones. For this problem, a classification robust equivalent weight function model based on the t-inspection statistics is proposed, which has better performance than the conventional equivalent weight function models in the case of no more than one gross error in a certain type of observations. However, in the case of multiple gross errors in a certain type of observations, the performance of the conventional robust Kalman filter based on the two kinds of equivalent weight function models are barely satisfactory due to the interaction between gross errors. To address this problem, an improved classification robust Kalman filtering method is further proposed in this paper. To verify and evaluate the performance of the proposed method, simulation tests were carried out based on the GPS/BDS data and their results were compared with those obtained with the conventional robust Kalman filtering method. The results show that the improved classification robust Kalman filtering method can effectively reduce the impact of multiple gross errors on the positioning results and significantly improve the positioning accuracy and reliability of PPP.

The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space Lq (Ω; ℝ^m), q > 1, with radius r and centered at the origin. The trajectory of the system is defined as p-integrable multivariable function from the space Lq (Ω; ℝⁿ), (1/q) + (1/p) = 1, satisfying the system’s equation almost everywhere. It is shown that the system’s trajectories are robust with respect to the fast consumption of the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource.

The paper presents a general concept of geodetic observations adjustment based on application of the Edgeworth' series and the principle of an alternative choice. The Edgeworth' series approximates the empirical distribution of measurement errors and gives an opportunity to modify the empirical characteristics of errors distribution. The method of estimation used is based on the principle of the alternative choice. Its natural robustness for outliers was the basis for newly created method called PAC-E. The paper presents the algorithm and some numerical tests that were carried out to compare the results of the proposed method with the results of the classical LS adjustment. Special attention was paid on the effect of non-zero excess and robustness of the proposed method.

The problem of outlying observations is very well-known in the surveying data processing. Outliers might have several sources, different magnitudes, and shares within the whole observation set. It means that it is not possible to propose one universal method to deal with such observations. There are two general approaches in such a context: data cleaning or robust estimation. For example, the robust M-estimation has found many practical applications. However, there are other options, such as R-estimation or the absolute M _split estimation. The latter method was created to be less sensitive to outliers than the squared M _split estimation (the basic variant of Msplit estimation). From the theoretical point of view, the absolute M _split estimation cannot be classified as a robust method; however, it was proved that it could be used in such a context under certain conditions. The paper presents the primary comparison between that method and a conventional robust M-estimation. The results show that the absolute M _split estimation predominates over the classical methods, especially when the percentage of outliers is high. Thus, that method might be used to process LiDAR data, including mismeasured points. Processing synthetic data from terrestrial laser scanning or airborne laser scanning confirms that the absolute M _{split / estimation can deal with outliers sufficiently.}

One of the most critical problems in all practical systems is the presence of uncertainties, internal and external disturbances, as well as disturbing noise, which makes the control of the system a challenging task. Another challenge with the physical systems is the possibility of cyber-attacks that the system’s cyber security against them is a critical issue. The systems related to oil and gas industries may also be subjected to cyber-attacks. The subsets of these industries can be mentioned to the oil and gas transmission industry, where ships have a critical role. This paper uses the Quantitative Feedback Theory (QFT) method to design a robust controller for the ship course system, aiming towards desired trajectory tracking. The proposed controller is robust against all uncertainties, internal and external disturbances, noise, and various possible Deception, Stealth, and Denial-of-Service (DOS) attacks. The robust controller for the ship system is designed using the QFT method and the QFTCT toolbox in MATLAB software. Numerical simulations are performed in MATLAB/Simulink for two case studies with disturbances and attacks involving intermittent sinusoidal and random behavior to demonstrate the proposed controller.

In the hybrid multiple H-bridge topology of beam supply, the load change of a DC/DC full-bridge converter can greatly affect the output voltage during onsite operation. An improved sliding mode control (SMC) strategy is thus proposed in this paper, where the rate of switching control is added to the law of system equivalent control to create a law that can realize a complete sliding mode control. Considering the special operating conditions of the load can have an influence on the performance of the controller, the impact of uncertainty existing in onsite conditions is suppressed with the proposed strategy utilized. The validity of the proposed strategy, finally, is verified by simulation, which proves the outperformance of the system in both robustness and dynamics.

This work proposes an optimum design and implementation of fractional-order Butterworth filter of order (1 + α), with the help of analog reconfigurable field-programmable analog array (FPAA). The designed filter coefficients are obtained after dual constraint optimization to balance the tradeoffs between magnitude error and stability margin together. The resulting filter ensures better robustness with less sensitivity to parameter variation and minimum least square error (LSE) in magnitude responses, passband and stopband errors as well as a better –3 dB normalized frequency approximation at 1  rad/s and a stability margin. Finally, experimental results have shown both lowpass and highpass fractional step values. The FPAA-configured outputs represent the possibility to implement the real-time fractional filter behavior with close approximation to the theoretical design.

In this article conclusions from nearly 10 years of collaboration with Polish and German Engineer-to-Order (ETO) small and medium-sized enterprises (SMEs) from mechanical sector was presented. Research objective was to highlight common organizational problems they are dealing with, which prevent them from transition to Mass Customizers. As a result, a concept of 5 foundations for robust process design was proposed: procedures, product selection, machining philosophy, planning and storage, cross-functional teams. More practical solutions from this field have to be published to fill the research gap.

A method of the improvement of the total station observations 3D adjustment by using precise geoid model is presented. The novel concept of using the plumb line direction obtained from the precise geoid model in combined GPS/total station data adjustment is applied. It is concluded that results of the adjustment can be improved if data on plumb line direction is used. Theoretical background shown in the paper was proved with an experiment based on the total station and GPS measurements referred to GRS80 geocentric reference system and with the use of GUGIK2001 geoid model for Poland.

Various components of surface texture are identified, namely form, waviness and roughness. Separation of these components is done by digital filtering. Several problems exist during analysis of two-process surfaces. Therefore the Gaussian robust profile filtering technique was established and has been studied here. The computer generated 2D profiles and 3D surface topographies having triangular scratches as well as measured stratified surfaces were subjected to filtration. However even robust filter applications cause distortion of profiles having valleys wider than 100 μm. In order to minimize the distortion associated with wide and deep valleys, the robust filter should be modified. A special procedure was elaborated for minimizing distortion of roughness profiles caused by filtration. Application of this method to analyses of several profiles was presented. The difference between 1-D and 2-D filtering of surface topography using the same kind of filter was discussed. As a result we found that modification of a 2-D surface topography filter was not necessary.

A robust Kalman filter improved with IGG (Institute of Geodesy and Geophysics) scheme is proposed and used to resist the harmful effect of gross error from GPS observation in PPP/INS (precise point positioning/inertial navigation system) tightly coupled positioning. A new robust filter factor is constructed as a three-section function to increase the computational efficiency based on the IGG principle. The results of simulation analysis show that the robust Kalman filter with IGG scheme is able to reduce the filter iteration number and increase efficiency. The effectiveness of new robust filter is demonstrated by a real experiment. The results support our conclusion that the improved robust Kalman filter with IGG scheme used in PPP/INS tightly coupled positioning is able to remove the ill effect of gross error in GPS pseudorange observation. It clearly illustrates that the improved robust Kalman filter is very effective, and all simulated gross errors added to GPS pseudorange observation are successfully detected and modified.